scholarly journals Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

2020 ◽  
Vol 36 (5) ◽  
pp. 637-648
Author(s):  
Asahi Tazaki ◽  
Shintaro Takeuchi ◽  
Suguru Miyauchi ◽  
Lucy T. Zhang ◽  
Ryo Onishi ◽  
...  
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Numerical Method ◽  
Linear Analysis ◽  
Tangential Component ◽  
Membrane Permeation ◽  
Permeate Flux ◽  
Permeable Membrane ◽  
Lubrication Equation ◽  
Inverse Effect

ABSTRACTTo understand the lubrication-dominated permeation through a membrane, numerical simulations of permeation through a moving corrugated permeable membrane is carried out with a fully validated numerical method. Through comparisons between the numerical results and the results of an asymptotic analysis of permeate flux (under an infinitesimal permeability condition) using Reynolds lubrication equation, the effect of permeation on lubrication and its inverse effect (i.e., the dependence of permeation on lubrication) are discussed. The linear and non-linear dependences of the relaxation of the lubrication pressure due to membrane permeation are identified. The effect of the tangential component of the permeate flux is evaluated by a linear analysis, and the limitation of Reynolds-type lubrication is discussed.

ON THE APPLICATION OF A NOVEL ALGORITHM TO HYDRODYNAMIC DIFFUSION AND VELOCITY FLUCTUATIONS IN SEDIMENTING SYSTEMS

1996 ◽  
Vol 07 (04) ◽  
pp. 543-561 ◽  
Author(s):  
WOLFGANG KALTHOFF ◽  
STEFAN SCHWARZER ◽  
GERALD RISTOW ◽  
HANS J. HERRMANN
Keyword(s):  
Numerical Simulations ◽  
Numerical Method ◽  
Incompressible Fluids ◽  
Strong Anisotropy ◽  
Velocity Fluctuations ◽  
Drag Forces ◽  
Large Numbers ◽  
Spatial Dimensions ◽  
Experimental Findings ◽  
Novel Algorithm

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.

scholarly journals Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes

2018 ◽  
Vol 849 ◽  
pp. 741-776
Author(s):  
Nils Tilton ◽  
Denis Martinand
Keyword(s):  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Radial Flow ◽  
Temporal Frequency ◽  
Outer Cylinder ◽  
Global Mode ◽  
Permeable Membrane ◽  
Global Modes ◽  
Taylor Couette ◽  
Base Flows

Variations in the local stability of the flow in a Taylor–Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy’s law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.

Critical design considerations for harnessing reverse osmosis processes in water/wastewater treatment

2006 ◽  
Vol 6 (6) ◽  
pp. 61-70 ◽  
Author(s):  
L.F. Song ◽  
K.G. Tay ◽  
G. Singh
Keyword(s):  
Mass Transfer ◽  
Membrane Fouling ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Full Scale ◽  
Driving Pressure ◽  
Feed Water ◽  
Permeate Flux ◽  
Membrane Channel ◽  
Permeable Membrane

In this paper, the performance of the full-scale RO process with highly permeable membranes and the governing mechanisms were carefully studied. It was found that the performance of a full-scale RO process could be controlled by two possible mechanisms, namely mass transfer rate and thermodynamic limitations. Under relatively low driving pressure, it was controlled by mass transfer rate (water flux) of the membrane. However, with the highly permeable membrane, it is possible that the performance is limited by the thermodynamic limitation, in which the osmotic pressure becomes equal to the driving pressure inside of the membrane channel. A process controlled by thermodynamic limitation is an extremely case of the hydraulic imbalance problem. When it occurs, it means part of the membranes in the processes do not contribute to permeate production. More complicated are situations in the intermediate pressure range, in which both mechanisms contribute to, but none of them can dominate, the performance of the process. Some innovative concepts and theories on the performance of the full-scale RO processes were developed. These concepts and theories may provide better qualitative explanations for the behaviors often observed in the full-scale RO processes. A better quantitative simulations or predictions of the performance of the process were developed upon these concepts and theories. Experiments were carried out on a pilot membrane process of 6 m membrane channel to imitate the performance of the full-scale RO under various conditions. The experimental performance data were compared with theoretical simulations and excellent agreement was obtained. Another focus of this current study was on characterization and modeling of membrane fouling in the full-scale RO process. Colloidal fouling experiments were conducted to study the fouling potential of feed water and a new fouling indicator was proposed. The indicator can be directly used in the mathematical model to simulate fouling development in the full-scale RO processes. Model simulations showed that under certain condition (thermodynamic restriction), the recovery or average permeate flux of a full-scale RO process would maintain a constant value even membrane fouling was taking place. Experimental verification of the simulation results is currently under way. With the new developments and findings in this area, methods or protocols for optimization of full-scale processes of the highly permeable RO membranes were suggested.

On thin evaporating drops: When is the -law valid?

2016 ◽  
Vol 792 ◽  
pp. 134-167 ◽  
Author(s):  
M. A. Saxton ◽  
J. P. Whiteley ◽  
D. Vella ◽  
J. M. Oliver
Keyword(s):  
Mass Transfer ◽  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Viscous Dissipation ◽  
Square Root ◽  
Vapour Transport ◽  
Asymptotic Results ◽  
Rate Of Evaporation ◽  
And Diffusion ◽  
Matched Asymptotic Analysis

We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip and diffusion-dominated vapour transport are taken into account. A matched asymptotic analysis in the limit of small slip is used to derive a generalization of Tanner’s law that takes account of the effect of mass transfer. We find a criterion for when the contact-set radius close to extinction evolves as the square root of the time remaining until extinction – the famous $d^{2}$-law. However, for a sufficiently large rate of evaporation, our analysis predicts that a (slightly different) ‘$d^{13/7}$-law’ is more appropriate. Our asymptotic results are validated by comparison with numerical simulations.

Investigation of the Asymptotic Behavior of Stresses at the Tip of Wedge- and Cone-Shaped Cracks

2012 ◽  
Vol 528 ◽  
pp. 119-126
Author(s):  
T. Korepanova ◽  
V.P. Matveenko ◽  
N. Sevodina
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Numerical Method ◽  
Stress Singularity ◽  
Singular Solutions ◽  
Different Boundary Conditions ◽  
Crack Faces ◽  
Made In

Numerical method is proposed for construction of singular solutions for spatial crossing wedge-and cone-shaped cracks. The results of numerical simulations made in the study allowed us to estimate the stress singularity indices at the tip of wedge-shaped cracks for different boundary conditions on the crack faces and at the tip of crossing cone cracks. The stress singularity at the tips of cone-shaped cracks is investigated.

The analysis and modelling of dilatational terms in compressible turbulence

1991 ◽  
Vol 227 ◽  
pp. 473-493 ◽  
Author(s):  
S. Sarkar ◽  
G. Erlebacher ◽  
M. Y. Hussaini ◽  
H. O. Kreiss
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Direct Numerical Simulations ◽  
Homogeneous Turbulence ◽  
Compressible Turbulence ◽  
Quasi Equilibrium ◽  
Compressible Mixing Layer

It is shown that the dilatational terms that need to be modelled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of the compressible velocity field, which generates these dilatational terms, is explored by asymptotic analysis of the compressible Navier-Stokes equations in the case of homogeneous turbulence. The lowest-order equations for the compressible field are solved and explicit expressions for some of the associated one-point moments are obtained. For low Mach numbers, the compressible mode has a fast timescale relative to the incompressible mode. Therefore, it is proposed that, in moderate Mach number homogeneous turbulence, the compressible component of the turbulence is in quasi-equilibrium with respect to the incompressible turbulence. A non-dimensional parameter which characterizes this equilibrium structure of the compressible mode is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

A Numerical Method for Penetration into Concrete Target Using SPH-Lagrange Coupling Method

2010 ◽  
Vol 163-167 ◽  
pp. 1217-1221 ◽  
Author(s):  
Xi Cheng Huang ◽  
Yi Xia Yan ◽  
Wei Zhou Zhong ◽  
Yu Ze Chen ◽  
Jian Shi Zhu
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Numerical Method ◽  
Empirical Equation ◽  
Maximum Depth ◽  
Coupling Method ◽  
Depth Of Penetration ◽  
Lagrange Method ◽  
Concrete Target

This paper demonstrates the application of both numerical simulation and empirical equation in predicting the penetration of a concrete target by an ogive-nosed projectile. The results from the experiment performed by Gran and Frew are used as a benchmark for comparison. In the numerical simulations a 3.0-caliber radius-head steel ogival-nose projectile with a mass of 47 kg is fired against cylindrical concrete target with a striking velocity of 315 m/s. In the simulation the smooth particles hydrodynamics SPH-Lagrange coupling method is applied to predict the maximum depth of penetration. For calculation of DoP and response of projectile the SPH-Lagrange method can give satisfactory results.

scholarly journals Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

2021 ◽  
Author(s):  
Suguru Miyauchi ◽  
Shuji Yamada ◽  
Shintaro Takeuchi ◽  
Asahi Tazaki ◽  
Takeo Kajishima
Keyword(s):  
Reynolds Number ◽  
Osmotic Pressure ◽  
Membrane Permeability ◽  
Flow Rate ◽  
Peclet Number ◽  
Concentration Polarization ◽  
Circular Pipe ◽  
Permeate Flux ◽  
Permeable Membrane ◽  
Péclet Number

AbstractA concise and accurate prediction method is required for membrane permeability in chemical engineering and biological fields. As a preliminary study on this topic, we propose the concentration polarization model (CPM) of the permeate flux and flow rate under dominant effects of viscosity and solute diffusion. In this model, concentration polarization is incorporated for the solution flow through a semi-permeable membrane (i.e., permeable for solvent but not for solute) in a circular pipe. The effect of the concentration polarization on the flow field in a circular pipe under a viscous-dominant condition (i.e., at a low Reynolds number) is discussed by comparing the CPM with the numerical simulation results and infinitesimal Péclet number model (IPM) for the membrane permeability, strength of the osmotic pressure, and Péclet number. The CPM and IPM are confirmed to be a reasonable extension of the model for a pure fluid, which was proposed previously. The application range of the IPM is narrow because the advection of the solute concentration is not considered, whereas the CPM demonstrates superior applicability in a wide range of parameters, including the permeability coefficient, strength of the osmotic pressure, and Péclet number. This suggests the necessity for considering concentration polarization. Although the mathematical expression of the CPM is more complex than that of the IPM, the CPM exhibits a potential to accurately predict the permeability parameters for a condition in which a large permeate flux and osmotic pressure occur.

Steady States of Sheared Active Nematics

2014 ◽  
Vol 6 (01) ◽  
pp. 75-86 ◽  
Author(s):  
Zhenlu Cui ◽  
Xiaoming Zeng ◽  
Jianbing Su
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Hydrodynamic Model ◽  
System Size ◽  
Complete Characterization ◽  
Steady States ◽  
Steady Shear

AbstractA continuum hydrodynamic model has been used to characterize flowing active nematics. The behavior of such a system subjected to a weak steady shear is analyzed. We explore the director structures and flow behaviors of the system in flow-aligning and flow tumbling regimes. Combining asymptotic analysis and numerical simulations, we extend previous studies to give a complete characterization of the steady states for both contractile and extensile particles in flow-aligning and flow-tumbling regimes. Another key prediction of this work is the role of the system size on the steady states of an active nematic system: if the system size is small, the velocity and the director angle files for both flow-tumbling contractile and extensile systems are similar to those of passive nematics; if the system is big, the velocity and the director angle files for flow-aligning contractile systems and tumbling extensile systems are akin to sheared passive cholesterics while they are oscillatory for flow-aligning extensile and tumbling contractile systems.

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